Statistical analysis by the EPI identifies several factors which the think tank says “undermine” the statistic’s “status as a fair comparison”.

In particular, the paper says, more than a quarter of the rise in pupils attending good or outstanding schools is accounted for by an absolute increase in pupil numbers and shifts in the schools which pupils attend.

This accounts for 578,000 of the increase, says the EPI.

“That is not to say we should write all of this off from the total,” say the authors.

“The Department for Education would rightly point out that it intended for higher performing schools to expand.”

David Laws was an education minister until 2015

In addition, the paper says, some 579,000 pupils attend schools rated good or outstanding but which have not been inspected since at least 2010.

Among these are 309,000 pupils at schools which converted to academies and have never have been inspected in their current form.

Again, the report acknowledges: “That is not to say that we should exclude these pupils from totals of those attending good or outstanding schools.

“If they had been inspected more recently they may well have achieved the same outcome,” the paper adds.

The authors also suggest that changing the old Ofsted “satisfactory” grade to “requires improvement”, which was seen as punitive, may have led to some inspectors awarding the “good” grade more readily.

Mr Laws said: “When you take into account rising pupil numbers, the large quantity of schools not inspected for many years, and the possible impact of a new Ofsted grading system, it is simply impossible for this statistic to bear the weight that ministers want to place on it.

“It would be better if the government stopped using this statistic, which misrepresents the level of improvement in school standards, and risks generating complacency about the education challenges the country faces.”

A Department for Education spokeswoman said: “The facts are clear. The vast majority of pupils are in good or outstanding schools across the country, 1.9m more than in 2010, and an increase from 66% to 86% over that time.

“Academic standards continue to rise, with more pupils reaching the expected standard in maths at the end of primary school and 154,000 more six year olds on track to become fluent readers since the phonics check was introduced in 2012.”